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A167700
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Number of partitions of n into distinct odd squares.
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12
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1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,1
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COMMENTS
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A167701 and A167702 give record values and where they occur: A167701(n)=a(A167702(n)) and a(m) < A167701(n) for m < A167702(n);
a(A167703(n)) = 0.
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for sequences related to sums of squares.
Vaclav Kotesovec, Graph - The asymptotic ratio
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FORMULA
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a(n) = f(n,1,8) with f(x,y,z) = if x<y then 0^x else f(x-y,y+z,z+8) + f(x,y+z,z+8).
G.f.: Product_{k>=0} (1 + x^((2*k+1)^2)). - Ilya Gutkovskiy, Jan 11 2017
a(n) ~ exp(3 * 2^(-7/3) * Pi^(1/3) * (sqrt(2)-1)^(2/3) * Zeta(3/2)^(2/3) * n^(1/3)) * (sqrt(2)-1)^(1/3) * Zeta(3/2)^(1/3) / (2^(7/6) * sqrt(3) * Pi^(1/3) * n^(5/6)). - Vaclav Kotesovec, Sep 18 2017
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EXAMPLE
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a(50) = #{49+1} = 1;
a(130) = #{121+9, 81+49} = 2.
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MATHEMATICA
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nmax = 100; CoefficientList[Series[Product[1 + x^((2*k-1)^2), {k, 1, Floor[Sqrt[nmax]/2] + 1}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 18 2017 *)
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PROG
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(Haskell)
a167700 = p a016754_list where
p _ 0 = 1
p (q:qs) m = if m < q then 0 else p qs (m - q) + p qs m
-- Reinhard Zumkeller, Mar 15 2014
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CROSSREFS
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Cf. A033461, A016754, A167661, A000700, A111900.
Sequence in context: A016373 A281815 A205988 * A010057 A204220 A281814
Adjacent sequences: A167697 A167698 A167699 * A167701 A167702 A167703
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KEYWORD
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nonn,look
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AUTHOR
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Reinhard Zumkeller, Nov 09 2009
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STATUS
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approved
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